(Duration: 90 minutes; Full score: 120)
1. Multiple choice questions: (3 points× 6 =18 points)
1. As shown in the figure, the mass of each weight in the right plate of the balance is 1g, so the value range of the mass m(g) of object A can be expressed as () on the number axis.
2. The following figure is a schematic diagram of pinhole imaging principle. According to the size marked in the picture, the length of the image CD formed by this candle in the cassette is ().
A.b.1/3cm C.1/2cm d. 1 cm
3. The correct proposition in the following propositions is ()
A. If x, -2x+3
B. Two straight lines are cut by the third straight line, and the same angle is equal.
D congruent graphics must be similar graphics, but similar graphics are not necessarily congruent graphics.
5. The chart below shows the frequency distribution histogram of heartbeat times per minute in a class of Senior Two (all times are integers).
It is understood that only five students in this class have their hearts beating 75 times per minute. Please observe the figure below and point out that the following statement is wrong ().
A. data 75 belongs to group 2.
The frequency of group B 4 is 0. 1.
D. data 75 must be an intermediate value.
6. Both Party A and Party B start from place A and arrive at place B by bike. It is known that the distance between the two places is 30 kilometers. Party A walks 3 kilometers more than Party B every hour and arrives 40 minutes earlier than Party B. ..
Let b walk x kilometers per hour, then the equation can be listed as ()
2. Fill in the blanks: (3 points× 6 =18 points)
7. Decomposition factor: x3-16x = _ _ _ _ _ _ _ _ _ _.
8. As shown in the figure, if AB//CD is known, ∠B=68o, ∠CFD=7 1o, ∠ FDC = _ _ _ _ _ _ _ degrees.
9. The same number of students in Class A and Class B took the same math test. The class average and variance are as follows:
10. Point P is a point different from A and B on the hypotenuse AB of Rt△ABC. Do a straight PE cut △ABC through point P, and the triangle thus cut is similar to △ABC. Please draw a straight line that meets the following conditions, and briefly explain the vertical or parallel positional relationship between the straight line PE and the edge of △ABC under the corresponding graph.
Location relationship: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
12. in △ABC, AB= 10.
Three. Drawing questions: (5 points)
13. Draw with compasses and straightedge, but don't write the method, and keep the trace of drawing.
When Xiao Ming makes the corner of the class for the whole class, he should enlarge the figure on the original picture so that the ratio of the new figure to the corresponding line segment of the original picture is 2: 1. Ask the students to help Xiao Ming finish the work.
4. Answer: (***79 points)
14.(7 points) Please simplify it first, and then choose a number that makes the original formula meaningful and you like to substitute in the evaluation:
15.(8 points) Solve the following inequality groups, express the solution set on the number axis, and write its integer solution.
16.(8 points) The cost of producing one kilogram of fructose in Xishui Food Factory is 24 yuan, and its sales plan is as follows:
Scheme 1: If it is directly sent to the sales department of our factory in this city for sale, the price per kilogram is 32 yuan, but the sales department needs to pay related expenses of 2400 yuan per month;
Option 2: If sold directly to local supermarkets, the ex-factory price is 28 yuan per kilogram.
If only one scheme can be sold every month, and each scheme can sell the products of that month every month, then suppose that the monthly sales volume of this factory is X kilograms.
(1) If you are the factory director, how should you choose the sales plan to make the factory get more profits in that month?
(2) When the factory director listened to the summaries of various departments, the sales minister said that the best scheme was adopted for sales every month, so good work performance was achieved. However, after seeing the report on the relationship between sales volume and profit in the first quarter sent by the accountant (as shown in the following table), the factory director found that the sales volume written in the report did not match the actual profit. Please find out the difference and calculate the actual sales in the first quarter.
17.(8 points) Hao Hao's mother bought several bottles of yogurt at Yunli Supermarket for 12.50 yuan, but she found that the same yogurt was cheaper in Yunli Supermarket than in 0.2 yuan. So, when she bought yogurt the next day, she went to Liqun Supermarket to buy it. As a result, she bought it for 18.40 yuan.
18.(8 points) The ideological and moral construction of minors has attracted more and more attention from the society.
In order to guide students to establish a correct concept of consumption, a youth research institute randomly investigated the amount of pocket money (the amount is integer yuan) of 0/00 students in a school in Dalian during the winter vacation.
According to 100 survey data, make frequency distribution table and frequency distribution histogram:
(1) Complete the frequency distribution table and frequency distribution histogram; In the table, a = _ _ _ _ _, b = _ _ _ _ _ _ and c = _ _ _ _ _ _
(2) The example of this question is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
(3) The Institute believes that students who spend more than 150 yuan should be advised to be thrifty. Of the 1000 students in this school, how many students should be advised to be frugal?
19.(8 points) (1) A classmate wants to measure the height of a tree with its shadow. At a certain moment, he measured the height of a column as 1 m and the length of the shadow as 0.9 m, but when he went to measure the shadow, he found that the upper part of the shadow fell on the CD on the wall. (pictured) He measured BC=2.7 meters.
Can you help him find out how tall the tree is?
(2) Can you help him find other measuring methods (ruler, benchmark and mirror) within 24 hours a day? Please draw a schematic diagram and combine it with your graphic description:
Experimental equipment used: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Line segment whose length needs to be measured: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
20.(8 points) A certain district raises funds 1.600 yuan, and plans to paint on the trapezoidal open space with the upper and lower floors of10m and 20m respectively for decoration.
As shown in the figure, (1) the unit price of the paint they sprayed in △AMD and △BMC areas is 8 yuan /m2. When the △AMD area is covered (shaded part in the figure), * * * cost 160 yuan. Please calculate the cost of covering △BMC area.
(2) If there are two brands of paints to choose from in other regions, and the unit prices are 12 yuan /m2 and 10 yuan /m2 respectively, which paint should I choose just after the raised funds are used up?
2 1.( 12 points) Explore and innovate:
As shown in the figure, there are two parallel straight lines AB and CD in the known plane, and P is the moving point outside the straight lines AB and CD in the same plane.
(1) When point P moves to the left of two points of the line segment AC between AB and CD, as shown in figure (1), what is the relationship between ∠P, ∠A and ∠C?
Please prove your conclusion:
(2) When the point P moves to the right of two points of the line segment AC between AB and CD, as shown in Figure (2), what is the relationship between ∠P, ∠A and ∠C? (No proof is required.
) a:
(3) With the movement of point P, can you find out the other two different positional relationships, draw corresponding graphs, and write the relationships between ∠P, ∠A and ∠C at this time? Choose one of them to prove it.
Practice and application:
Fold a rectangular piece of paper ABCD (as shown in the figure) along EF, so that point B falls on B 1, point C falls on C 1, and point B 1C 1 meets point G. Fill in the blanks according to the above conclusions:
22.( 12 points) Factorization with geometric figures, through the combination of numbers and shapes, can help us understand the problem well.
(1) For example, add an appropriate number to the horizontal line below to make it completely flat.
As shown above, "x2+8x" is based on a square with a side length of x, plus two small rectangles with a length of x and a width of 4.
In order to make it completely flat (that is, the figure becomes a square), a small square with a side length of 4 must be added.
That is x2+8x+42=(x+4)2.
Please draw a picture on the horizontal line below and explain the practice of x2-4x+_ _ _ _ = (x-_ _ _ _) 2 in words and fill in the blanks.
Description:
(2) It is known that the sum of the areas of a square with a side length of x and a rectangle with a length of x and a width of 8 is 9. Look at the picture and find the side length of x: (add the corresponding numerical or algebraic expressions to the letters a, b, c and x).
a = _ _ _ _ _ _ _ _ _ _ _ _，B=_______
c = _ _ _ _ _ _ _ _ _ _ _ _，x=_______
(3) The complete square formula can be expressed by the area of plane geometry. In fact, some algebraic formulas can also be decomposed in this form, such as using the area decomposition factor: a2+4ab+3b2,
So: a2+4ab+3b2=(a+b)(a+3b).
Write an algebraic expression with letters A and B, draw a geometric figure, and write the result of factorization with geometric figures.
Provide the following three kinds of graphics: a square with side lengths A and B, and a rectangle with length A and width B (use each at least once).
Test answer
First, multiple-choice questions:
1.A 2。 D 3。 D 4。 B 5。 D 6。 B
Tip:
1. 1
2.
5.25+20+9+6=60 people
A: 69.5 & lt75 & lt79.5 ∴75 belongs to the second group.
B: The frequency of the fourth group is 6.
D: The median is between 69.5 and 79.5, but not necessarily 75.
6. solution: the speed of b is X km/h, and the speed of a is (x+3) km/h.
2. Fill in the blanks:
7.8.4 1 9.b
10.
British Columbia or PE⊥AC PE⊥BC or PE⊥AB.
1 1.- 1 12.50
Tip:
8. Solution:
9.
1 1. solution: multiply both sides of the equation by x-5.
12. Solution:
3. Painting problems:
13. The method is not unique, as long as it is reasonable.
4. Answer questions:
14. Solution:
15. Solution:
16.( 1) Solution: Let scheme 1 profit be y 1 yuan, and scheme 2 profit be y2 yuan.
The actual sales volume should be 2 100kg.
17. Solution: Her mother bought X bottles of yogurt in Yunli supermarket for the first time.
It is proved that x=5 is the root of the listed equation.
A: I bought five bottles of yogurt at Yunli Supermarket for the first time.
18.( 1) 10,25,0.25
(2) The amount of students' winter vacation pocket money in a school in Dalian 100.
(3)1000× (0.3+0.1+0.05) = 450 people.
19.( 1) solution: let the tree height AB be x meters.
(2) Rulers and benchmarks; Morality, Policy and BC
20. Solution:
Choose a German brand paint, and just use up the raised funds.
2 1.( 1) Proof: P is PE//AB.
Practice and application: 90 270
22.( 1)22 2
Note: "X2-4x" is regarded as subtracting two small rectangles with side length X and width 2 from the area of a square with side length X. In order to make it completely flat (that is, the figure becomes a square), a small square with side length 2 must be added, that is, X2-4x+22 = (x-2) 2.
(2)x+4； 4; 25; 1
(3)a2+2ab+b2=(a+b)2